Gravity-Fed Intravenous Infusion Without Pumps, Made Accurate: An Error Budget for the Standard Drip Set and a Constant-Head Mariotte Insert Design

Gravity-fed intravenous infusion is set once by counting drops and then drifts. For 1,000 mL of 0.9% saline prescribed at 125 mL/h, a fluid-physics model gives a standard drip set finishing at 99.0 mL/h (-20.8%), taking 8.97 h instead of 8.00 h, with a root-sum-square error budget of 22.7% across head decay, temperature, venous pressure, posture and drop-factor terms. A Mariotte-bottle constant-head insert costed at US$2.30 removes the head-decay term (residual 0.84%; bag in 8.07 h), but reaches 9.5% total error only if the clamp is set at the patient after fitting. Design study; simulated, not measured.